Cavani had been tipped for a possible move to England, with Chelsea and Mancheser City said to be previously preparing bids for the Uruguayan striker who has scored 49 goals over two seasons for the Partenopei.
In a press conference on the cusp of Friday's transfer deadline club president Aurelio De Laurentiis quipped: "Cavani has made a life decision and wants to go to Manchester, he has a plane waiting for him."
As Cavani sat beside him giggling, the 25-year-old striker replied: "I'm not going, I'm staying in Naples and I thank the president, who has made a significant effort."
An extra year has been added to Cavani's existing contract meaning it will now not expire until 2017. It also includes a buy-out clause of 60million euros, according to the club.
De Laurentiis added: "We chose to revise the existing contract instead of buying another striker because we know Edinson and bringing in a new player could also undermine the balance of the dressing room."
Cavani's decision to stay with Napoli comes despite his wife being mugged in Naples last year.
De Laurentiis said: "Let's show (them) that Naples is a good place to live."
Napoli, the Italian Cup holders, lost to Serie A champions Juventus in the Italian Super Cup in Beijing last month.
Source: AFP
Source: AFP